Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model

We introduce and analyze a quantum spin/Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit, but manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.Comment: 5+3 pages. v2: added three short appendices, including numerics comparing various four-fermi perturbation

Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.Comment: 48 pages, 9 figure

Purchasing Power Parity: The Irish Experience Re-visited

This paper looks at issues surrounding the testing of purchasing power parity using Irish data. Potential difficulties in placing the analysis in an I(1)/I(0) framework are highlighted. Recent tests for fractional integration and nonlinearity are discussed and used to investigate the behaviour of the Irish exchange rate against the United Kingdom and Germany. Little evidence of fractionality is found but there is strong evidence of nonlinearity from a variety of tests. Importantly, when the nonlinearity is modelled using a random field regression, the data conform well to purchasing power parity theory, in contrast to the findings of previous Irish studies, whose results were very mixed.

Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity

This paper draws attention to the limitations of the standard unit root/cointegration approach to economic and financial modelling, and to some of the alternatives based on the idea of fractional integration, long memory models, and the random field regression approach to nonlinearity. Following brief explanations of fractional integration and random field regression, and the methods of applying them, selected techniques are applied to a demand for money dataset. Comparisons of the results from this illustrative case study are presented, and conclusions are drawn that should aid practitioners in applied time-series econometrics.

Exploring Long Memory and Nonlinearity in Irish Real Exchange Rates using Tests based on Semiparametric Estimation

Deciding whether a time series that appears nonstationary is in fact fractionally integrated or subject to structural change is a difficult task. However, various tests have recently been introduced for distinguishing long memory from level shifts and nonlinearity. In this paper, three testing approaches based on the properties of semiparametric estimators of the fractional differencing parameter, d, are described and applied to the (log) Ireland-United Kingdom and Ireland-Germany real exchange rates. The two exchange rates behave quite differently over time and the new tests give different results for each; but overall the results provide fairly strong support for the possibility of nonlinearity rather than long memory.Fractional integration, long memory, nonlinearity, real exchange rates, struc- tural change

Modelling Ireland’s exchange rates: from EMS to EMU

This paper attempts to model the nominal and real exchange rate for Ireland, relative to Germany and the UK from 1975 to 2003. It offers an overview of the theory of purchasing power parity (PPP), focusing particularly on likely sources of nonlinearity. Potential difficulties in placing the analysis in the standard I(1)/I(0) framework are highlighted and comparisons with previous Irish studies are made. Tests for fractional integration and nonlinearity, including random field regressions, are discussed and applied. The results obtained highlight the likely inadequacies of the standard cointegration and STAR approaches to modelling, and point instead to multiple structural changes models. Using this approach, both bilateral nominal exchange rates are effectively modelled, and in the case of Ireland and Germany, PPP is found to be valid not only in the long run, but also in the medium term. JEL Classification: C22, C51, F31, F41fractional Dickey-Fuller tests, multiple structural changes models, purchasing power parity, random field regression, smooth transition autoregression

The structure, dynamics and interactions of the von Willebrand factor C3 domain

Von Willebrand factor (VWF) is a multimeric haemostatic protein comprised of a series of repeat domains. It is responsible for platelet adhesion to the site of vessel injury, binding to collagen exposed by injury and to platelets by glycoprotein Ibα (GPIbα). It also acts as a carrier for coagulation Factor VIII (FVIII), increasing its half-life in circulation and localising activated FVIII to the site of injury. Synthesised primarily in the endothelial cells, VWF multimers are either released constitutively into the bloodstream or ultra-large multimers are stored in the endothelial cell cytoplasm in cylindrical storage granules, Weibel-Palade bodies. The importance of VWF function on maintaining normal haemostasis is demonstrated by the quantitative and qualitative defects exhibited by von Willebrand disease (VWD), the most common inherited bleeding disorder in the world. Type 1 VWD is most common, caused by specific mutations throughout the multimeric protein and characterised by reduced levels of circulating VWF. Of the 6 C-terminal C domains of VWF, C3 contains the most VWD Type 1 causing mutations. Whilst the molecular structures of other domains which comprise the collagen, GpIbα and FVIII binding sites are well characterised, the C domain structures remain largely unsolved. This thesis presents the structure of the VWF C3 domain solved using nuclear magnetic resonance spectroscopy and the effect of specific disulphide bond mutations on the domain structure. The C3 domain is comprised of two distinct subdomains – SD1 and SD2. SD1 is dominated by two β-sheet structures whilst SD2 comprises a single β-sheet structure. Domain stability is maintained by five disulphide bonds, two in each subdomain and the inter-subdomain relationship preserved by a single disulphide bond connecting the two. Mutations of each individual disulphide bond resulted in incomplete folding of the domain, highlighting their importance in maintaining the structural integrity of the C3 domain